Commandino, Federico - Liber de centro gravitatis solidorum

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1uel coni portionis axis à centro grauitatis ita diui
ditur, ut pars, quæ terminatur ad uerticem reli
quæ partis, quæ ad baſim, ſit tripla.

Sit pyramis, cuius baſis triangulum abc; axis de; & gra
uitatis centrum K. Dico lineam dk ipſius Ke triplam eſſe.
trianguli enim bdc centrum grauitatis ſit punctum f; trian
guli adc centrum g; & trianguli adb ſit h: & iungantur af,
b g, ch. Quoniam igitur centrum grauitatis pyramidis in axe

conſiſtit: ſuntque de, af, bg, ch eiuſdem pyramidis axes: conue
nient omnes in idem punctum k, quod eſt grauitatis centrum.
Itaque animo concipiamus hanc pyramidem diuiſam in
quatuor pyramides, quarum baſes ſint ipſa pyramidis

57[Figure 57]
triangula; & axis pun
ctum k quæ quidem py
ramides inter ſe æquales
ſunt, ut demonſtrabitur.
Ducatur enim per lineas
dc, de planum ſecans, ut
ſit ipſius, & baſis abc com
munis ſectio recta linea
cel: eiuſdem uero & trian
guli adb ſit linea dhl. erit linea al æqualis ipſi
lb: nam centrum graui
tatis trianguli conſiſtit
in linea, quæ ab angulo
ad dimidiam baſim per
ducitur, ex tertia deci
ma Archimedis.
quare

triangulum acl æquale
eſt triangulo bcl: & propterea pyramis, cuius baſis trian
gulum acl, uertex d, eſt æqualis pyramidi, cuius baſis bcl

triangulum, & idem uertex. pyramides enim, quæ ab eodem

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